The DFT approach, in its static and time-dependent formulations, has been probed to be
a realistic method for studying a strongly-correlated quantum fluid as liquid helium;[1]} it has been shown to
sustain complex dynamical mechanisms, such as vortex nucleation and vortex-density waves interactions and,
as shown in the following, vortex reconnections. The Gross-Pitaevskii (GP) approach[2]} has been also shown
to sustain these effects in dilute cold gases. In particular,
slow collisions of two confined Bose-Einstein condensates (BEC) in both ground and exited states,
have been addressed within this approach.[3]}
